About magnetic properties of superfluid neutron matter with spin-triplet anisotropic p-wave pairing in superstrong magnetic fields and at supranuclear densities

Magnetic properties of a dense superfluid neutron matter (relevant to the physics in cores of magnetars, namely the strongly magnetized neutron stars) at supranuclear densities n > n₀ (where n₀ = 0.17 fm^–3 is the saturation nuclear density) with generalized Skyrme effective forces (with three density-dependent terms) and with spin-triplet anisotropic p-wave pairing (similar to ³He-A in magnetic fields, i.e. with spin S = 1 and orbital moment L = 1 of anisotropic Cooper pairs of neutrons) in the presence of a superstrong magnetic field (exceeding the 10¹⁷ G) are studied within the framework of the non-relativistic generalized Fermi-liquid theory at zero temperature. The upper limit for the density range of a neutron matter is restricted by the magnitude 3n₀ in order to avoid the account of relativistic corrections growing with density. The approximate general formula (valid for any parameterization of the Skyrme forces) is derived here analytically for the magnetic susceptibility (which contains additional correction depending nonlinearly on superstrong magnetic field H and on the density n) of a superfluid neutron matter in the limit of zero temperature. The obtained general formula for magnetic susceptibility is specified for the generalized BSk21 parameterization of the Skyrme forces and figures for corresponding values are plotted on the interval 1.5n₀ ≤ n ≤ 3n₀ and for superstrong magnetic fields 2⋅10¹⁷ G ≤ H ≤ 2⋅10¹⁸ G. It is established that the high-density ferromagnetic instability is removed in neutron matter with the generalized Skyrme forces (in particular, with the generalized BSk21 parameterization) not only in normal, but also in superfluid neutron matter with spin-triplet anisotropic p-wave pairing at supranuclear densities and in superstrong magnetic fields.